cp's OEIS Frontend

A177083 A006093(k)-fold repetition of A001248(k), k=1,2,3,..

%I A177083 #10 Mar 30 2012 18:52:05
%S A177083 4,9,9,25,25,25,25,49,49,49,49,49,49,121,121,121,121,121,121,121,121,
%T A177083 121,121,169,169,169,169,169,169,169,169,169,169,169,169
%N A177083 A006093(k)-fold repetition of A001248(k), k=1,2,3,..
%C A177083 Consider the initial terms of numerator sequences (dropping initial zeros) of
%C A177083 3; A005563=N(1) ,
%C A177083 5,3; A061037=N(2) ,
%C A177083 7,16,1; A061039=N(3) ,
%C A177083 9,5,33,3; A061041=N(4) ,
%C A177083 11,24,39,56,3; A061043=N(5) ,
%C A177083 13,7,5,4,85,1; A061045=N(6) ,
%C A177083 15,32,51,72,95,120,3; A061047=N(7) ,
%C A177083 17,9,57,5,105,33,161,3; A061049=N(8) ,
%C A177083 19,40,7,88,115,16,175,208,1; N(9),
%C A177083 21,11,69,6,1,39,189,14,261,3; N(10),
%C A177083 23,48,75,104,135,168,203,240,279,320,3; N(11)
%C A177083 One must add the following associated (minimum) squares (taken from squared entries in A172038) to these values to reach the next possible square not larger than the entry itself:
%C A177083 1;    N(1)
%C A177083 4,1;    N(2)
%C A177083 9,9,0;     N(3)
%C A177083 16,4,16,1;    N(4)
%C A177083 25,25,25,25,1;   N(5)
%C A177083 36,9,4,0,36,0;    N(6)
%C A177083 49,49,49,49,49,49,1;   N(7)
%C A177083 64,16,64,4,64,16,64,1, ; N(8)
%C A177083 Only if the index of N(.) is a prime we obtain a string of equal consecutive terms in these complementary rows: 4, 9, 25, 49, 121, 169..
%C A177083 The current sequence lists the consecutive complementary squares, A001248, in the rows with prime index, including their multiplicity (which is A006093).
%C A177083 This generates a link between the primes and the Rydberg-Ritz spectrum of the hydrogen atom.
%Y A177083 Cf. A072055, A135177.
%K A177083 nonn,easy
%O A177083 1,1
%A A177083 _Paul Curtz_, Dec 09 2010